Problem:
If m and b are real numbers and mb>0, then the line whose equation is y=mx+b cannot contain the point
Answer Choices:
A. (0,1997)
B. (0,−1997)
C. (19,97)
D. (19,−97)
E. (1997,0)
Solution:
Since mb>0, the slope and the y-intercept of the line are either both positive or both negative. In either case, the line slopes away from the positive x-axis and does not intersect it. The answer is therefore (1997,0). Note that the other four points lie on lines for which mb>0. For example, (0,1997) lies on y=x+1997;(0,−1997) lies on y=−x−1997;(19,97) lies on y=5x+2; and (19,−97) lies on y=−5x−2.